Although motor tasks at most times do not require much attention, there are findings that attention can alter neuronal activity not only in higher motor areas but also within the primary sensorimotor cortex. However, these findings are equivocal as attention effects were investigated only in either the dominant or the nondominant hand; attention was operationalized either as concentration (i.e., attention directed to motor task) or as distraction (i.e., attention directed away from motor task), the complexity of motor tasks varied and almost no left-handers were studied. Therefore, in this study, both right- and left-handers were investigated with an externally paced button press task in which subjects typed with the index finger of the dominant, nondominant, or both hands. We introduced four different attention levels: attention-modulation-free, distraction (counting backward), concentration on the moving finger, and divided concentration during bimanual movement. We found that distraction reduced neuronal activity in both contra- and ipsilateral primary sensorimotor cortex when the nondominant hand was tapping in both handedness groups. At the same time, distraction activated the dorsal frontoparietal attention network and deactivated the ventral default network. We conclude that difficulty and training status of both the motor and cognitive task, as well as usage of the dominant versus the nondominant hand, are crucial for the presence and magnitude of attention effects on sensorimotor cortex activity. In the case of a very simple button press task, attention modulation is seen for the nondominant hand under distraction and in both handedness groups.